Spin-Seebeck Temperature Sensors - IEEE Xplore

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Spin-Seebeck Temperature Sensors Tianjun Liao, Zhuolin Ye, and Jincan Chen

Abstract — The conceptual designs of two nanoscale spin-Seebeck temperature sensors are proposed based on the longitudinal spin-Seebeck effect (LSSE) in bilayers made of a ferromagnetic insulator Y3 Fe5 O12 and a Pt, and the transverse spin-Seebeck effect) in Ni81 Fe19 /Pt structure. The working principles of two sensors are presented. The direct conversion of the temperature information into the electric voltage is described in detail. Moreover, the effect of the spin Hall angle on the performance of sensors is discussed. The results obtained here reveal that the LSSE and TSSE have the potential to realize practical temperature sensors.

Fig. 1. Schematic of a temperature sensor based on the LSSE.

Index Terms — Inverse spin-Hall effect (ISHE), longitudinal, sensors, spin-Seebeck effect, transverse.

II. LSSE T EMPERATURE S ENSOR I. I NTRODUCTION

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HE discovery of the spin-Seebeck effect (SSE) in combination with spintronics offers new strategies to design nanoscale devices such as the power device [1], valve [2], 2-D position sensor [3], photodetector [4]–[6], and diode [7]. It was recently reported that heat flux can be flexibly measured based on the longitudinal SSE (LSSE) [8]. Especially, it was first reported in 2010 that the SSE can be applied to design temperature sensors [9]. However, there are few research works about the SSE temperature sensors. Several types of temperature sensors such as dual-mode AlN-on-silicon micromechanical resonator-based self-temperature sensors [10], P-type metal–oxide–semiconductor tunneling temperature sensors [11], p-i-n diode-based linear temperature sensors [12], and fiber Bragg grating sensors [13] have been proposed in the last years. Nowadays, many fields including nanoscale systems need the accurate temperature measurements. Hence, it is significant to further develop novel temperature sensors. In this paper, we conceptually propose two nanoscale SSE temperature sensors, which are based on the LSSE in bilayers made of a ferromagnetic insulator (FI) Y3 Fe5 O12 and a Pt, and the transverse SSE (TSSE) in Ni81 Fe19 /Pt structure. The results obtained will demonstrate that these concepts may provide new means for temperature measurements at nanoscale.

Manuscript received March 5, 2017; accepted April 4, 2017. The review of this paper was arranged by Editor M. M. Cahay. This work was supported by the National Natural Science Foundation under Grant 11675132 and 973 Program 2012CB619301, China. (Corresponding author: Jincan Chen.) The authors are with the Fujian Key Laboratory of Semiconductors and Applications, Collaborative Innovation Center for Optoelectronic Semiconductors and Efficient Devices, Department of Physics, Xiamen University, Xiamen 361005, China (e-mail: [email protected]). Color versions of one or more of the figures in this paper are available online at http://ieeexplore.ieee.org. Digital Object Identifier 10.1109/TED.2017.2691762

Based on the LSSE [14], [15], an LSSE temperature sensor composed of a FI Y3 Fe5 O12 , a normal metal Pt, and an external magnetic field H is designed, as shown in Fig. 1, where α is the angle between the magnetization M and the magnetic field H , L and W are the length and width of the FI/Pt bilayer, d N is the thickness of Pt, TH is the temperature of the heat source, and TL is the temperature of the cold reservoir. α is usually very small and taken as zero in the following calculation. The working mechanism is that when the sensor is attached to the heat source and the external magnetic field H is applied to the x-direction, the temperature difference between FI and Pt induces a part of the heat flow JQ to convert into a spin current JS , and simultaneously, a transverse electric field E ISHE and voltage V = E ISHE L are generated by means of the inverse spin-Hall effect (ISHE) as a result of the spin-orbit interaction. Because the Onsager symmetry can be reflected by a linear response matrix, the spin current and average heat flow over the FI/Pt interface are given by [1], [16], [17] G S −μ S /2e Js L S T = (1) JQ T /T T LST K + LS S

where T = TH − TL , L S is the interface spin-Seebeck coefficient, μs = μ↑ − μ↓ is the spin accumulation, μ↑ and μ↓ are the spin-up and spin-down electrochemical potentials, S = SS T is the spin-Peltier coefficient due to the Onsager reciprocity, T = [TH + TL ]/2, SS = L S /G S is the spin-Seebeck coefficient, G S is the interface spin-injection conductance, and K is the thermal conductance coefficient in the FI/Pt interface. The relation between the transverse charge current density jc (z) = Jc (z)/(d N W ) and the spin current density js (z) = Js (z)/A inside the normal metal at distance z induced by the ISHE can be given by [1], [16], [17] jc (z) = θSH js (z) × mˆ

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where A = LW is the area of the FI/Pt, mˆ is the spinpolarization vector, and θSH is the spin Hall angle. The spin current and charge current densities in the normal metal can be given by [1], [16], [17] ∂(μc /e)/∂y 1 θSH jc (3) = −σ N ∂(μs /2e)/∂z js −θSH 1 where μc = (μ↑ + μ↓ )/2 is the charge electrochemical potential and σ N is the spin conductivity. The spin accumulation μs obeys the spin-diffusion equation in the normal metal [1], [16], [17], that is ∇ 2 μs = μs /λ2N

(4)

where λ N is the spin-flip relaxation length. By using boundary conditions js (z = 0) = JS /A and js (d N ) = 0, the solution of the spin-diffusion equation can be expressed as

1 λN z z μs = + G N cosh θSH V G S sinh 2e a1 L λN λN λN dN − z − L S T cosh − θSH V G N (5) L λN where a1 = G S cosh((d N /(λ N )))+G N sinh((d N /(λ N ))), V = −((L/e))(∂μc /(∂y)) is the induced transverse voltage, and G N = σ N (W L/(λ N )) is the spin conductance. By using (1)–(5), the relation between the average transverse charge current Jc and the transverse voltage V in the Pt is derived as dN 1 Jc = jc d N W dz dN 0 2 λ V a3 θSH dN dN V G N λN L S N − θSH T tanh − = L a2 2λ N L L

Fig. 2. (a) TH as a function of the measured Voc for dN = 5 nm and TL = 300 K. (b) Dependent relation between Voc /ΔT and dN /λN for three given values of θSH , where GN /A = 1015 Ω −1 m−2 , GS /A = 6×1013 Ω −1 m−2 , LS /A = 4×109 AK-1 m−2 , L = 5 nm, and λN = 5 nm.

(6) where a2 = G N + G S coth(d N /(λ N )), a3 = (G S + 2G N tanh[d N /(2λ N )]/(G N + G S coth[d N /λ N ])). When the circuit is opened, Jc = 0 and the open voltage Voc is given by [16] L L S θSH T dN . (7) tanh Voc = 2 2λ N a2 λ(d N /λ + θSH a3 ) For a sensor that material and structure parameters are known, we can calculate the values of TH by measuring Voc and using (7), as shown in Fig. 2(a), where d N /λ N = 1 is chosen. Fig. 2(a) shows that TH is proportional to Voc for a given θSH . Because of the increase of TH , the temperature difference TH − TL increases, resulting in the increase of Voc . Using (7), we can prove that when θSH = (d N /(λ N a2 ))1/2 = 1.10, (TH −TL ) attains its minimum value for a given Voc . Nevertheless, the experimental values [18]–[20] of θSH reported in literature are much less than 1.10, and consequently, the values of θSH are selected in the region of θSH < 1.10 in this paper. Fig. 2(a) shows that in the region of θSH < 1.10, TH − TL is a monotonically decreasing function of θSH for a given Voc . It indicates that we can measure the temperature that changes only small scale. The spin Hall angle θSH is an important parameter in spintronic. Improving θSH is an issue to design

Fig. 3. Schematic of the TSSE temperature sensor.

high-performance nanoscale devices, which need to further develop the material science. Fig. 2(b) depicts the dependent relation between Voc /T and d N /λ N . It is seen from Fig. 2(b) that when d N /λ N is close to 0.5, we can obtain the maximum value of Voc /T , i.e., the maximum temperature sensitivity. It shows that the choice of d N /λ N is a key issue to design the actual sensor. When d N /λ N is very small, which increases the difficulty of making the sensor because of the limit of the present nanotechnology. In practice, d N /λ N should be chosen to be larger than 0.5 but not suitable for too large. The cause is that when d N is much larger than the spin-diffusion length λ N , we cannot measure the temperature because the spin current and spin voltage disappear [9]. III. TSSE T EMPERATURE S ENSOR Fig. 3 shows a schematic of the TSSE temperature sensor composed of a Pt wire and a Ni81 Fe19 film. The Pt wire is

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attached on the left upper side of the Ni81 Fe19 film. The left and right sides of the Ni81 Fe19 film are, respectively, contacted with the cold reservoir at temperature TL and the hot reservoir at temperature TH , where TL is the constant temperature that we want to detect. The intrinsic mechanism of this temperature sensor is that when a magnetic field H to be greater than the coercive force HC and a temperature gradient ∇T are applied along the x-direction, the spinup and spin-down electrons with electrochemical potentials μ↑ and μ↓ generate in Ni81 Fe19 . The spin accumulation μ↑ − μ↓ drives a spin current J s flowing into Ni81 Fe19 across the Ni81 Fe19 /Pt interface. By means of the ISHE, the electric field EISHE generated by the spin current J s along they-direction can be expressed as [9], [17] EISHE = θSH ρ N J s × σ

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where ρ N is the electric resistivity in Pt and σ is the spinpolarization vector. The spin accumulation μ↑ − μ↓ induced at the higher temperature end of the Ni81 Fe19 layer with the temperature difference T = TH − TL is given by [9], [17] μ↑ − μ↓ = eSS T /2

(9)

where SS is the SSE coefficient and e is the elementary positive charge. Because of the ISHE, the spin voltage injects spins into the Pt layer and generates the electric voltage V , which can be expressed as [21] θSH ηNiFe-Pt L N V = E ISHE L N = − (μ↑ − μ↓ ) (10) e dN where L N is the length of Pt and ηNiFe-Pt is the spin-injection efficiency, which can be calculated by [21], [22]

σ N λ F tanh(d N /λ N ) −1 sinh2 [d N /(2λ N )] 1+ ηNiFe-Pt = cosh(d N /λ N ) σ F λ N tanh(d F /λ F ) (11) where d F and λ F denote the thickness and relaxation length of Ni81 Fe19 , and σ N and σ F are the electrical conductivity of the Pt and Ni81 Fe19 . By using (9) and (10), the electric voltage V is derived as V = −θSH ηNiFe-Pt (L N /d N )SS T /2.

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Using (12), we can generate the curves of TH varying with the measured electric signal V , as depicted in Fig. 4. It is seen from Fig. 4 that TH is a monotonically decreasing function of the absolute value of V . For a given TH , the value of V decreases as θSH decreases. Using the relationship between the temperature and the electric signal, we can determine the temperature TH . Fig. 4(b) depicts the dependent relation between V /T and d N /λ N for a given θSH . It is seen from Fig. 4(b) that when d N /λ N is close to 1.3, we can obtain the maximum value of V /T , i.e., the maximum temperature sensitivity. Similarly, the choice of d N /λ N is also a key issue to design the actual TSSE temperature sensor.

Fig. 4. (a) TH as a function of the measured V. (b) Dependent relation between Voc /ΔT and dN /λN for three given values of θSH , where dN /λN = 1.5, dF /λF = 2, SS = −3 × 10−11 VK−1 , LN /dN = 4 × 105 , λN = 5 nm, λF = 5 nm, σN = 1.1 × 106 Sm−1 , σF = 2.9 × 106 Sm-1 , and TL = 300 K.

IV. C OMPARISON OF T WO T EMPERATURE S ENSORS Figs. 2(a) and 4(a) show that the temperature measurement ranges of the two temperature sensors are all from 27° to 70 °C. However, the electric voltage of the LSSE temperature sensor is larger than that of the TSSE temperature sensor for same given values of θSH , TH , and d N /λ N . Figs. 2(a) and 4(a) indicate that the electric voltage signals of two sensors are microvolt. The larger the electric voltage of the sensor is, the smaller the error caused by the measurement and the higher the accuracy of the voltmeter. This means that the fabrication of the LSSE temperature sensor is easier than that of the TSSE temperature sensor. It is seen from Figs. 2(b) and 4(b) that the tendency of V /T varying with d N /λ N in the LSSE temperature sensor is similar to that in the TSSE temperature sensor. However, the optimal values (d N /λ N )opt of d N /λ N at the maximum values of V /T are different from each other. Obviously, (d N /λ N )opt of the TSSE temperature sensor is larger than that of the LSSE temperature sensor. For any one of the two temperature sensors, the value of d N /λ N should be chosen to not be less than their respective (d N /λ N )opt so that the fabrication difficulty of the temperature sensor may be reduced. It is also seen from Figs. 2(b) and 4(b) that in the rational regions and for the same value of d N /λ N , V /T of the LSSE temperature sensor is larger than that of the TSSE temperature sensor. This means that the performance of the LSSE temperature sensor is better than that of the TSSE temperature sensor, and consequently, the LSSE temperature sensor can be more conveniently exploited in the practical applications.

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V. C ONCLUSION In a word, we have presented two approaches to design temperature sensors using the longitudinal LSSE and TSSE and clearly described their working mechanisms. The electric voltage was found to be proportional to the temperature. The results obtained here shows that the conceptually proposed sensors may provide new ways for temperature measurements. R EFERENCES [1] A. B. Cahaya, O. A. Tretiakov, and G. E. W. Bauer, “Spin Seebeck power generators,” Appl. Phys. Lett., vol. 104, no. 4, p. 042402, Jan. 2014. [2] F. K. Dejene, J. Flipse, and B. J. Van Wees, “Spin-dependent Seebeck coefficients of Ni80 Fe20 and Co in nanopillar spin valves,” Phys. Rev. B, Condens. Matter, vol. 86, no. 2, p. 024436, Jul. 2012. [3] K. Uchida, A. Kirihara, M. Ishida, R. Takahashi, and E. Saitoh, “Local spin-seebeck effect enabling two-dimensional position sensing,” Jpn. J. Appl. Phys., vol. 50, no. 12R, p. 120211, Dec. 2011. [4] K. Ando, M. Morikawa, T. Trypiniotis, Y. Fujikawa, C. H. W. Barnes, and E. Saitoh, “Direct conversion of light-polarization information into electric voltage using photoinduced inverse spin-Hall effect in Pt/GaAs hybrid structure: Spin photodetector,” J. Appl. Phys., vol. 107, no. 11, p. 113902, Jun. 2010. [5] G. Isella, F. Bottegoni, A. Ferrari, M. Finazzi, and F. Ciccacci, “Photon energy dependence of photo-induced inverse spin-Hall effect in Pt/GaAs and Pt/Ge,” Appl. Phys. Lett., vol. 106, no. 23, p. 232402, Jun. 2015. [6] K. Ando, M. Morikawa, T. Trypiniotis, Y. Fujikawa, C. H. W. Barnes, and E. Saitoh, “Photoinduced inverse spin-Hall effect: Conversion of light-polarization information into electric voltage,” Appl. Phys. Lett., vol. 96, no. 8, p. 082502, Feb. 2010. [7] Z.-Q. Zhang, Y.-R. Yang, H.-H. Fu, and R. Wu, “Design of spinSeebeck diode with spin semiconductors,” Nanotechnology, vol. 27, no. 50, p. 505201, Dec. 2016. [8] A. Kirihara et al., “Flexible heat-flow sensing sheets based on the longitudinal spin Seebeck effect using one-dimensional spin-current conducting films,” Sci. Rep., vol. 6, p. 23114, Mar. 2016. [9] K. Uchida et al., “Observation of the spin Seebeck effect,” Nature, vol. 455, no. 7214, pp. 778–781, Oct. 2008. [10] J. L. Fu, R. Tabrizian, and F. Ayazi, “Dual-mode AlN-on-silicon micromechanical resonators for temperature sensing,” IEEE Trans. Electron Devices, vol. 61, no. 2, pp. 591–597, Feb. 2014. [11] Y.-K. Lin and J.-G. Hwu, “Role of lateral diffusion current in perimeterdependent current of MOS(p) tunneling temperature sensors,” IEEE Trans. Electron Devices, vol. 61, no. 10, pp. 3562–3565, Oct. 2014. [12] S. Rao, G. Pangallo, and F. G. Della Corte, “4H-SiC p-i-n diode as highly linear temperature sensor,” IEEE Trans. Electron Devices, vol. 63, no. 1, pp. 414–418, Jan. 2016. [13] L. Men, P. Lu, and Q. Chen, “A multiplexed fiber Bragg grating sensor for simultaneous salinity and temperature measurement,” J. Appl. Phys., vol. 103, no. 5, p. 053107, Mar. 2008. [14] K.-I. Uchida, H. Adachi, T. Ota, H. Nakayama, S. Maekawa, and E. Saitoh, “Observation of longitudinal spin-Seebeck effect in magnetic insulators,” Appl. Phys. Lett., vol. 97, no. 17, p. 172505, 2010. [15] Z. Qiu, D. Hou, K. Uchida, and E. Saitoh, “Influence of interface condition on spin-Seebeck effects,” J. Phys. D, Appl. Phys., vol. 48, no. 16, p. 164013, Apr. 2015. [16] T. Liao, J. Lin, G. Su, B. Lin, and J. Chen, “Optimum design of a nanoscale spin-Seebeck power device,” Nanosc., vol. 7, no. 17, pp. 7920–7926, May 2015. [17] A. B. Cahaya, O. A. Tretiakov, and G. E. W. Bauer, “Spin Seebeck power conversion,” IEEE Trans. Mag., vol. 51, no. 9, pp. 1–14, Sep. 2015.

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Tianjun Liao received the M.S. degree from Huaqiao University, Quanzhou, China, in 2014. He is currently pursuing the Ph.D. degree with Xiamen University, Xiamen, China. He has authored several papers in international journals, such as Nanoscale, International Journal of Thermal Sciences, the Journal of Power Sources, Applied Physics Letters, and Energy Conversion and Management. His current research interests include solar cells and thermodynamic theory.

Zhuolin Ye received the B.S. degree from Nanchang University, Nanchang, China, in 2016. He is currently pursuing the M.S. degree with Xiamen University, Xiamen, China. He has authored several papers in international journals, such as Physics Review E and Communications in Theoretical Physics. His current research interests include solar cells and thermodynamic theory.

Jincan Chen received the Ph.D. degree from the University of Amsterdam, Amsterdam, The Netherlands, in 1997. He is currently a Professor with the Department of Physics, Xiamen University, Xiamen, China. He has authored more than 340 papers in international journals. His current research interests include solar cells, thermoelectric devices, fuel cells, and quantum thermodynamic cycles.